If you'd like to do pull it off just like in the example you showed, then I would recommend using a screen recording software (for the highest quality video) and a Photoshop graphic of an X Box controller just like the PS3 controller graphic shown in the example you posted.
When it comes to screen recording software you have three options: the best is the HD PVR from Hauppage: http://www.hauppauge.com/site/products/data_hdpvr.html. This is the best option due to the fact that it comes with a processor inside the unit that can capture your footage at 1080i using Component HD cables and convert it straight to H.264 video that you can edit in Sony Vegas Pro 12. This also means that you won't have to rely on a computer which can cause frame delays if the machine starts running slowly. The only drawback to this option is the price; it goes for around $180 at Best Buy. However, you should be able to find a better deal somewhere online.
Your next best screen capture software will be the Blackmagic Intensity Pro (if your computer has a card slot) or Intensity Shuttle (if your computer has USB 3.0): http://www.blackmagicdesign.com/products/intensity/. Both can record up to 1080p video on your computer which can be edited in Sony Vegas Pro 12. The Intensity Pro has an HDMI and VGA option, and the Intensity Shuttle has a Component option so they should both work for the X Box. I have used the Shuttle before and have found it to be very reliable with a solid computer system. It currently goes for around $199.
Lastly, you can use the VGA2USB: http://www.epiphan.com/products/frame-grabbers/vga2usb/. The VGA2USB is a frame grabber that can record video from a VGA source. The best part about this hardware is that it comes with a VGA splitter, allowing you to monitor your footage on a television while recording to a computer through the VGA2USB adapter. From what I can see online, it seems like a solid piece of equipment. The biggest problem with this piece of hardware is it's price: $300.
Next, to show your viewers which buttons you're pressing to achieve a skill move in FIFA 13, I would suggest using the same graphic layout that your sample video had This is because the controller graphic is good at clearly showing which buttons to press for a skill move, whereas a video of your fingers performing the move may have your audience missing some of the action due a bad angle of the camera. To achieve this, find a graphic of both the top and the front of an XBOX 360 controller. Then, using Photoshop, use the "Pen" or mask selection tool and draw a mask around the controller. Then, turn your mask into a selection and press the Backspace or Delete key to get rid of the background that your downloaded controller graphic might have. Next, draw a new mask with the pen tool around one of the buttons on the controller. Once you've done this, and before changing tools, click the black/white circle at the bottom of the Layer panel in Photoshop and choose "Solid Color" from the dropdown menu. This will create a solid color over that button within the mask that you created. Double click the layer to open the Layer Styles window and check the Color Overlay box. Selecting the Color Overlay text, change the color of your Color Overlay to yellow. Lastly, turn down the opacity of the button layer you just created to about 30-50 percent. This way, you can still see the text of the button behind your yellow mask selection. If this sounds confusing, I've also found a link to clipping masks in the Photoshop website: http://helpx.adobe.com/photoshop/using/masking-layers.html.
Do the same for each of the buttons on the controller until you have a layer for every button. Then save the PSD and import it into Sony Vegas 12 as layers. This way the PSD will come in with each layer on a different video track (which will allow you to turn the button highlights on and off using opacity). Combine your footage recorded from FIFA 13 and you should be all set to go!
I hope this helps! Please feel free to ask me to go into more detail for some of the steps that I've listed. I know it's a lot to take in and I'm not always the best at explaining things!